Question

Convert given fraction into fractions with equal denominators:
$\left(iii\right)$ $\frac{4}{5},\frac{17}{20},\frac{23}{40}$and $\frac{11}{16}$

Answer 1

Finding $LCM$ of denominators $5,20,40$ and $16$:

$LCM$ of $5,20,40$ and $16:$

$\begin{array}{cc}2\mid & 5,20,40,16\\ 2\mid & 5,10,20,8\\ 2\mid & 5,5,10,4\\ 2\mid & 5,5,5,2\\ 5\mid & 5,5,5,1\\ \mid & 1,1,1,1\end{array}$

$LCM$ of $5,20,40,16=2\times 2\times 2\times 2\times 5=80$

Equalizing the denominators of the given fractions.

As the $LCM$ is $80$, therefore let’s make the denominator same as $80$ in each fraction as follows:

By multiplying $16$ in numerator and denominator in the $1^{st}$ fraction we get,

$\frac{4}{5}\Rightarrow \frac{4\times 16}{5\times 16}=\frac{64}{80}$

By multiplying $4$ in numerator and denominator in the $2^{nd}$ fraction we get,

$\frac{17}{20}\Rightarrow \frac{17\times 4}{20\times 4}=\frac{68}{80}$

By multiplying $2$ in numerator and denominator in the $3^{rd}$ fraction we get,

$\frac{23}{40}\Rightarrow \frac{23\times 2}{40\times 2}=\frac{46}{80}$

By multiplying $5$ in numerator and denominator in the $4^{th}$ fraction we get,

$\frac{11}{16}\Rightarrow \frac{11\times 5}{16\times 5}=\frac{55}{80}$

Hence, the given fractions with equal denominators are $\frac{64}{80},\frac{68}{80},\frac{46}{80}$, and $\frac{55}{80}$